I'd say Tonga would be better. Lay up in Vava'u (Neiafu - Port of Refuge). It's well protected and said to be a good even in cyclones, which will always be a risk in this area. Nuku'alofa, the capital and main town, is much more open, and not as pretty either. Vava'u is reasonable well served for yachties.
Tonga's a great place, safe, the people are friendly (as Cook said), it's stable and you can get most everyday things. The sailing around Vava'u is supposed to be fantastic. Tongatapu to the south (Nuku'alofa) is somewhat less interesting, but you should still drop in there.
Jealous...

Sydney to NZ you should have no problem timing your trip with a favourable weather window. You will likely go round the top end rather than via the Strait. Forecast will be pretty accurate as it is based not only on computer models but also on land-station observations.

NZ to Tonga is a different pair of goggles and can be a rough passage at times. Read up on what the perils are and time your departure according to the weather rather than to any other objectives.